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Question Number 28676 by abdo imad last updated on 28/Jan/18

$$letgive{u}_n={\int }_{n\pi }^{(n+1)\pi }{e}^{-\lambda t}\frac{sint}{\sqrt{t}}with\lambda >0$$ $$calculate\sum _{n=0}^{+\mathrm{\infty }}{u}_n.$$ $$$$

Commented byabdo imad last updated on 30/Jan/18

$$\sum _{n=0}^{+\mathrm{\infty }}{u}_n={\int }_0^{\mathrm{\infty }}{e}^{-\lambda t}\frac{sint}{\sqrt{t}}dt=\sqrt{\pi }sin(\frac{\pi }{4}-\frac{arctan\lambda }{2})from$$ $$Q28756.$$

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